Quantum coherence and entanglement are two fundamental quantum features that reflect different manifestations of the same principle–the superposition principle.
We will focus on them to explore their connections with extractable work.
Coherence of the battery is characterized by the minimum relative entropy \(S(\rho _b(t)||\delta )\)  of \(\rho _b(t)\)  with respect to all incoherent states \(\delta \in \mathcal {I}\)  [1]}:
\(C(t)=\min _{\delta \in \mathcal {I}}S(\rho _b(t)\Vert  \delta )=S_{\Delta }(t)-S(t),\) 
